Noether symmetry and non-Noether conserved quantity of the relativistic holonomic nonconservative systems in general Lie transformations |
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Authors: | Luo Shao-Kai |
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Institution: | Institute of Mathematical Mechanics and Mathematical Physics, Zhejiang Sci-Tech University, Hangzhou 310018, China; Key Laboratory of Advanced Textile Materials and Manufacturing Technology (Zhejiang Sci-Tech University), Ministry of Education, Hangzhou 310018, China |
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Abstract: | For a relativistic holonomic nonconservative system, by using the
Noether symmetry, a new non-Noether conserved quantity is given under
general infinitesimal transformations of groups. On the basis of the
theory of invariance of differential equations of motion under
general infinitesimal transformations, we construct the relativistic
Noether symmetry, Lie symmetry and the condition under which the
Noether symmetry is a Lie symmetry under general infinitesimal
transformations. By using the Noether symmetry, a new relativistic
non-Noether conserved quantity is given which only depends on the
variables $t$, $q_s $ and $\dot {q}_s $. An example is given to
illustrate the application of the results. |
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Keywords: | relativity holonomic
nonconservative system Noether symmetry non-Noether conserved
quantity |
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